The impact of small groups on pre‐ and postcopulatory sexual selection in polyandrous populations

Abstract Sexual selection is a key evolutionary force but varies widely between populations. Two key factors that influence sexual selection are the extent to which females copulate with multiple males (polyandry) and variation in the social environment. Increasing research demonstrates populations are structured by complex socio‐sexual networks, and the structure of these networks can influence sexual selection by shaping the relationship between male precopulatory mating success and the intensity of postcopulatory competition. However, comparatively less attention has been dedicated to the influence of group structure on sexual selection and how differences in the size of groups may impact on the relative force of pre‐ and postcopulatory sexual selection in polyandrous populations. The presence of groups (i.e., group structure) and the size of groups varies widely in nature and forms an implicit part of much experimental sexual selection research under laboratory conditions. Here I use simulations of mating competition within populations that vary in the size of groups they contain, to show that variation in group size, and in particular small groups, can influence sexual selection. Specifically, I show that null expectations for the operation of pre‐ and postcopulatory sexual selection is governed by the size of groups within populations because smaller group sizes constrain the structure of sexual networks leading to reinforcing episodes of pre‐ and postcopulatory sexual selection. Given broad variation in group structure in nature and the tendency for experimental sexual selection research to study replicate small groups, these effects have implications for our understanding of the operation of sexual selection in polyandrous populations.


| INTRODUC TI ON
Sexual selection arises from competition between members of the same sex to fertilize the gametes of the opposite sex and is responsible for a vast array of ornaments, weapons, and behaviors (Andersson, 1994;Darwin, 1871;McCullough et al., 2016). Over the last 50 years our understanding of sexual selection, and how it varies between populations, has been advanced by two key developments. First, is the realization that when females copulate with multiple males over the time fertilization occurs (i.e., are polyandrous), sexual selection on males continues after mating, forcing males to compete not only over the number and fecundity of mates but also over the proportion of their mate's ova that they fertilize (Eberhard, 2009;Parker, 1970;Parker & Birkhead, 2013;Pizzari & Wedell, 2013;Simmons & Wedell, 2020). Second, is the growing understanding that patterns of sexual selection are strongly dependent on variation in the social environment (Clutton-Brock, 2017;Emlen & Oring, 1977;Lyon & Montgomerie, 2012;Maldonado-Chaparro et al., 2018;McDonald et al., 2013;West-Eberhard, 1983).
The impact of the social environment on sexual selection has long been recognized, including variation in operational sex ratios and population density (Emlen & Oring, 1977;Janicke & Morrow, 2018;Kokko & Rankin, 2006). More recently, research has further demonstrated that animal populations are structured by complex social and sexual networks (Albery et al., 2021;Beck et al., 2021;Krause et al., 2014;Maldonado-Chaparro et al., 2018;McDonald et al., 2019McDonald et al., , 2020Muniz et al., 2015;Oh & Badyaev, 2010;Ryder et al., 2008;Silk & Hodgson, 2021;Smith et al., 2023). The structure of such sociosexual networks (i.e., the patterning of sexual interactions among individuals) can influence sexual selection by shaping the relationship between male precopulatory mating success and the intensity of postcopulatory competition he faces (Fisher et al., 2016;Greenway et al., 2021;McDonald et al., 2013;McDonald & Pizzari, 2018;Muniz et al., 2015;Sih et al., 2009;Wey & Kelly, 2019). For example, if more polygynous males mate with on average the least polyandrous females (negative mating assortment) this can create a positive covariance between male mating success and male paternity share, because males successful in precopulatory competition may also face the lowest intensity of postcopulatory competition (McDonald & Pizzari, 2016;Sih et al., 2009). Such patterns are expected to accentuate the benefits of increased mating success (i.e., Bateman gradients) and accentuate sexual selection (Greenway et al., 2021;McDonald & Pizzari, 2018). Alternatively, if the males with the highest mating success copulate with the most polyandrous females (positive mating assortment), they may suffer the most intense postcopulatory competition. These patterns may reduce the overall variance in male reproductive success and indicate trade-offs between pre-and postcopulatory competitiveness (Fisher et al., 2016;McDonald & Pizzari, 2018), promoting the emergence of alternative male reproductive tactics (Kvarnemo & Simmons, 2013). Patterns of mating assortment in nature and in captive populations have the potential to vary widely (Fisher et al., 2016;Greenway et al., 2021;McDonald & Pizzari, 2018;Morimoto et al., 2019;Wey & Kelly, 2019) and preliminary investigations suggest these patterns of mating assortment may be related to both the size of mating groups and levels of polyandry (McDonald & Pizzari, 2018). Assessing under what scenarios we may expect sexual networks to show positive, negative or no assortment is therefore an important step in understanding the conditions that determine whether episodes of sexual selection reinforce or oppose each other (Evans & Garcia-Gonzalez, 2016;Greenway et al., 2021;McDonald, Spurgin, et al., 2017;McDonald & Pizzari, 2018;Morimoto et al., 2019).
In invertebrates, intrasexual competition and mating may occur within restricted small subunits with only a handful or few dozen of individuals, such as within the local demes of forked fungus beetles (Bolitotherus cornutus) and other insects (Formica et al., 2011;Greeff & Ferguson, 1999), as well as small local aggregations of hermaphroditic barnacles and leeches (Tan et al., 2004;Wilkialis & Davies, 1980). Such group structure is also an implicit component of much of sexual selection research under laboratory conditions, where small groups are experimentally constructed and where mating and competition is restricted to within these small groups (De Lisle & Svensson, 2017).
For example, experimental studies of the impacts of polyandry in fowl (Gallus gallus) have used groups ranging from 3 males and 4 females to 10 males and 12 females (Collet et al., 2012;McDonald, Spurgin, et al., 2017;Roth et al., 2021). In mammals, experimental investigations of sexual selection have used group sizes of 2 females and 2-4 males (Mills et al., 2007), while studies in fish and reptiles have investigated the effects polyandry, sex ratios, and density on sexual selection in groups ranging from 2 to 60 individuals (Aronsen et al., 2013;Devigili et al., 2015;Fitze & Le Galliard, 2008;Head et al., 2008;Wacker et al., 2013). In invertebrates, the group sizes employed also vary between model species, including 5 individuals in hermaphroditic snails and flatworms (Hoffer et al., 2017;Marie-Orleach et al., 2016;Pélissié et al., 2014), from 3 males and 3 females to 16 males and 16 females in Drosophila species (Bateman, 1948;Bjork & Pitnick, 2006;Gowaty et al., 2012;Morimoto et al., 2019;Pischedda & Rice, 2012), 10 males and 10 females in Squash bugs (Greenway et al., 2021) and 20 males and 20 females in swordtail crickets (Laupala cerasina; Turnell & Shaw, 2015). As a result, many sexual selection studies implicitly emulate populations structured into groups, whether assessing patterns of sexual selection within groups or overall patterns of selection across groups (De Lisle & Svensson, 2017). While the consequences of constraining interactions in animal social networks to within small groups has been considered in terms of patterns of infectious disease transfer (Nunn et al., 2015;Sah et al., 2018)

| MATERIAL S AND ME THODS
To explore the impact of different group sizes on sexual networks and the relationship between pre-and postcopulatory sexual selection, I first constructed artificial populations of 18 males and 18 females. In each population, individuals mated within small groups of three males and three females with one of five predefined mating distributions that differed in average polyandry (i.e., the mean number of male mating partners per female) ranging from 1.67 to 2.67 mates per female, and also differed in the standardized variance in male mating success (i.e., the opportunity for precopulatory sexual selection, I M = VAR M ∕ M 2 ; Appendix 1). The range of average polyandry utilized here is biologically relevant given both behavioral and extra-pair paternity studies indicate that the average number of mates per female often ranges between 1 and 2 males in primates Reichard, 1995), in birds (Brekke et al., 2013;Dunn et al., 2009;Fiske & Kålås, 1995;Grinkov et al., 2022;Krietsch et al., 2022;Webster et al., 1995;Wetton et al., 1997), as well as in studies of polyandrous spiders and reptiles (Levine et al., 2015;Watson, 1998)  mixed-effects models using package "lme4" (Bates et al., 2015).

| RE SULTS
Across all levels of polyandry, SCIC was significantly lower and was restricted to negative values when males competed in small groups, compared to medium and larger groups, where variation in SCIC was larger and spanned both positive and negative values ( Figure 2a, Table 1). There was a significant interaction between group size and polyandry ( 2 2 = 87.174, p < .001, Table 1   where average female polyandry is three male mates per female, this may represent strong sperm competition levels regardless of TA B L E 1 Linear mixed-effects model results for the effects average polyandry and group size on the sperm competition intensity correlation (SCIC), the standardized covariance between mating success and paternity share (COV MP ) and the maximum potential precopulatory selection gradient (Jones index whether the population is unstructured or is divided into local mating groups of three males and three females. However, in the population structured into groups of three males and three females, there would be no variation in male mating success, and variation in male reproductive success would instead be driven only by postcopulatory mechanisms. Crucially, such group sizes and levels of polyandry are not unusual in both nature and experimental settings (e.g., Bjork & Pitnick, 2006;Collet et al., 2012;Collias & Saichuae, 1967;House et al., 2019;Krause & Ruxton, 2002;Mills et al., 2007;Morimoto et al., 2019;Oklander et al., 2014). The results here indicate that the strongest impact of group structure should be observed when sexual competition is consistently limited to within small groups either via experiment or in natural populations. In nature a wide variety of factors can place limits on the size of groups within populations. For example, foraging strategy, prey density, predation pressure, ecological constraints, social competition, and risk of infectious disease spread, may all restrict the minimum and maximum size of groups (Chapman & Chapman, 2000;Creel et al., 2014;Hamilton, 1971;Janson, 1988;Kasozi & Montgomery, 2020;Lucchesi et al., 2020;Markham et al., 2015;Nunn et al., 2015;Szemán et al., 2021;Takada & Washida, 2020;Teichroeb & Sicotte, 2009). However, in many natural populations group membership may be more temporally fluid. For example, when extra-group matings are common and/or multiple groups are more highly interconnected (e.g., Cant et al., 2002;Carpenter et al., 2005;Lucchesi et al., 2020) or when females visit and copulate at multiple leks rather than mating within one lek (Hess et al., 2012;Schroeder, 1991). This movement and mating between groups may effectively increase the size of the group in which competition occurs. When competition and mating is sufficiently fluid between social groups, the scale at which competition occurs will instead more closely match that of non-group structured more openly mixed population. As a result, if group sizes in nature are typically larger than those used in experiments, the results here suggest scope for a potential disconnect between patterns of pre-and postcopulatory sexual selection observed in laboratory experiments and patterns expected in larger natural groups.

| DISCUSS ION
Finally, while I have discussed the impact of increasing polyandry on patterns of sexual selection on males in populations that vary in group structure, group structure may itself impact on levels of polyandry. For example, the division of populations into smaller groups may favor an increase in female polyandry to avoid the negative consequences of local group male infertility (Dean et al., 2010).
Alternatively, if males that copulate frequently are more spermlimited (Warner et al., 1995;Wedell et al., 2002)-all else being equal-successful males structured within small groups may be comparatively less sperm-limited than successful males in unstructured populations where access to mates is less restricted. As a result, small group sizes may reduce female sperm limitation and disfavor increases in polyandry. Understanding the frequency of such alternate scenarios my provide new insights into the potential coevolution of group size and polyandry.

ACK N OWLED G M ENTS
I thank Tommaso Pizzari for many discussions in the development of this work and Sozos Michaelides for comments on an earlier draft.
GCM was funded by a Young Researcher Excellence Program fellowship from the Hungarian National Office for Research, Development, and Innovation (FK134741).

CO N FLI C T O F I NTER E S T S TATEM ENT
The author declares no competing interests. For all levels of polyandry, the scope for variation in SCIC is limited by smaller groups versus larger groups, resulting in more positive COV MP and a steeper M in small groups.